m=1 (1+(m-1))(1+(m-2))(1-)z
(1+m)(1+(m-1))(1-)z-1 .

On the other hand the Laplace transform of \( g_{1} \)  is the Mittag-Leffler function \( E_{\gamma }(\cdot ) \) , see [1]}
\(L_{1}(z) = \frac{1}{z} E_{\gamma }\big (-\tfrac{1}{\Gamma (1-\gamma )z}\big ) .\) 
